Book: Incompleteness: The Proof and Paradox of Kurt Godel
Author: Rebecca
Goldstein
Year published: 2005
Date finished: 2013
Genre: Biography
Rating:10/10
Review:
Rebecca Goldstein thinks like a philosopher and writes like a novelist, which is not surprising because she is both. And so, she begins Incompleteness not with Godel's birth, nor with abstract accounts of what he did, but with two friends walking near the Institute for Advanced Studies in Princeton, NJ.
One friend is elderly, about 70, rumpled and with a mane of white hair. The other is much younger and much more formally dressed. Every once in a while, the older man stops and looks at his younger friend with an expression of disbelief. The older man is Albert Einstein. The younger one is Kurt Godel. At about this time, Einstein was asked why he went to work each day and replied "for the pleasure of walking home with Godel".
What did Godel do?
Kurt Godel's work changed the foundations of mathematics. Essentially, he showed that no formal system that is large enough to contain all of arithmetic can proven to be consistent; and that no formal system can prove itself to be consistent. This is important because, at the end of the 19th century and beginning of the 20th, cracks were appearing in the foundations of math. It was shown that there could be consistent non-Euclidean geometries; later, Bertrand Russell showed that there were paradoxes in set theory. One attempt to repair the foundations was formalism, which tries to reduce math to a formal system. The most famous champion of this approach was David Hilbert; Russell and Alfred North Whitehead wrote Principia Mathematica to try to build all of math from a very basic formal system.
Kurt Godel not only showed that PM had flaws, he showed that any such system would necessarily have flaws. This was the end of formalism.
What Godel did not do
Godel's work has been claimed by various post-modernists and mystics as showing that math is personal and that it's all just theories. In Incompleteness, Rebecca Goldstein demolishes these claims. Godel was a Platonist. In fact, she makes the case that the fundamental reason for the friendship between Einstein and Godel was that they were both Platonists - and that they were the only two Platonists at the Institute. Formalism attempts to make math internal and self-contained. Godel believed that math is really "out there"; that it reflects not only the everyday reality we all live in, but the deeper reality of the ideal forms as postulated by Plato.
How strange was Godel?
No biography of Godel would be complete without a description of just how strange he was. As an elderly main Godel was clearly paranoid. He starved himself to death because he thought he was being poisoned. He thought doctors were conspiring against him. But, even much earlier in life, he was decidedly odd. Highly averse to confrontation, he never wanted to say anything for which he did not have absolute proof; thus, he sat in meetings of the Vienna Circle, with whom he radically disagreed, and never said a word. Incompleteness has many more stories of the oddness of Godel.
Summary
I strongly recommend this book to anyone interested in math, logic or philosophy. It is beautifully written and, considering the complexity of the thoughts it describes, remarkably lucid.
About the Author: Goldstein is a philosopher (PhD from Princeton) and a novelist..
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